Opponents of the nuclear agreement with Iran see it as a license for Tehran to wreak havoc in the region. Freed from economic pressure and flush with financial resources, the thinking goes, Iran can be expected to unleash its emboldened minions upon Israel and Arab states and undermine U.S. interests. However, contrary to what the critics say, the nuclear deal is far more likely to curb Iran’s regional ambition. It is rather the instability that would follow the failure of the deal that...